It was discovered in 2002 that the painting in the Caracas museum that was thought to be Matisse's Odalisque in Red Trousers was a fake. Photograph: Afp/AFP/Getty Images

For the curators of Venezuela's most prestigious modern art museum, the recent reappearance of a Matisse that was stolen from their collection more than a decade ago ought to have been cause for joy and relief.

A former director and an investigative journalist have raised concerns about the works that may be missing, some of which are estimated to be worth as much as $3m (£2m). They claim these are signs of deeper problems, including a lack of transparency, inadequate supervision and personal animosities at an institution that was once deemed among the leading contemporary art centres in Latin America, but has struggled since its founder, Sofía Imber, was sacked by the Venezuelan president, Hugo Chávez, live on public television.

The theft of the Odalisque was the biggest indication of problems at the museum, which was founded in 1973 and became a symbol of the country's oil wealth. Matisse's depiction of a semi-nude, dark-haired woman, which hung in a place of honour, was stolen at some point and replaced by a fake that was discovered in 2002.

It remained missing until last month, when the FBI arrested two suspects – Cuban Pedro Antonio Marcuello Guzman and Mexican María Martha Elisa Ornelas Lazo– who had allegedly been trying to sell the picture to undercover FBI agents for $740,000.

For the former director of the museum, Rita Salvestrini, the investigation in Miami has brought back doubts she raised in 2002 about the running of the museum that she took over after Imber was fired.

After discovering the Matisse hanging on the walls was a fake, Salvestrini ordered a series of full inventory checks. When she realised several pieces were missing, she called in an external auditor, who reported that 14 works – including Jasper Johns's Brooms and a piece by Soto that once hung behind her predecessor's desk – were unaccounted for. In addition, close to 200 other works were uncatalogued. "Both instances were equally alarming because they reflect that none of the controls were being followed," Salvestrini said.

"To me the findings [of the auditor] should have been used to correct a situation but the museum became a place where people's answers were designed to confuse and not to clarify," she said.

It was unclear whether the 14 pieces were temporarily misplaced or stolen, but efforts to track them down came to little.

One work, an etching by Freud, was purchased from the Timothy Taylor gallery in London, but appears not to have arrived at the museum. The London gallery said it had sold 55 Freud etchings to the Caracas museum between 1998 and 2001, "all of which were invoiced to the museum and shipped directly as per instruction".

Marinela Balbi, author of The Kidnap of the Odalisque, said there were 365 discrepancies in the number of works catalogued and accounted for at the museum. "These were institutions that were managed as if they were private, even though they are public. There was no accountability, or controls," said Balbi, who added that the tumult caused by the sacking of the founder also created a period of confusion that thieves may have exploited. After the sacking of Imber "there was a lot of institutional uncertainty coupled with a certain carelessness in inventory practices and a permissiveness in moving works to and from the museum", she said.

The museum denies any of its works are missing.

"Works of art get stolen all the time … Until the FBI reports its findings it would be irresponsible to speculate," said Adriana Meneses Imber, former director of the Jacobo Borges Museum and the daughter of the MACCSI founder. She said: "With the change in administration from my mother to the other person, an inventory was conducted and they said several pieces were missing. That is completely untrue."

The museum did not respond to repeated requests by the Guardian to be shown the works said to be "unaccounted for". On a recent visit there were very few pieces from its permanent collection on display – although Picasso's Suite Vollard etchings were among them.